To establish trust with a pet lizard, it's important to start by providing a comfortable and secure environment for it. Spend time near the lizard's enclosure to allow it to get used to your presence without feeling threatened. Slowly introduce handling by starting with short periods of gentle interaction, such as letting the lizard crawl onto your hand. Be patient, consistent, and gentle in your approach to help build trust over time. Offer treats as positive reinforcement and always respect the lizard's boundaries to create a trusting bond.